Exploring Volume: Concepts and Calculations

What is the volume of a cube with side length 3 cm?

• 9 cm³

• 27 cm³

• 18 cm³

• 12 cm³

Answer explanation

The volume of a cube is calculated using the formula V = side³. For a cube with a side length of 3 cm, V = 3 cm × 3 cm × 3 cm = 27 cm³. Therefore, the correct answer is 27 cm³.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Which of the following is a unit of volume?

• Square meter

• Cubic meter

• Meter

• Square centimeter

Answer explanation

Cubic meter is a unit of volume, measuring three-dimensional space. In contrast, square meter and square centimeter are units of area, while meter is a unit of length.

Tags

CCSS.5.MD.C.3A

CCSS.5.MD.C.3B

CCSS.5.MD.C.4

Convert 2 liters to milliliters.

• 200 ml

• 2000 ml

• 20 ml

• 20000 ml

Answer explanation

To convert liters to milliliters, multiply by 1000. Therefore, 2 liters x 1000 = 2000 milliliters. The correct answer is 2000 ml.

Tags

CCSS.4.MD.A.1

Estimate the volume of a small water bottle that holds about 500 ml of water.

• 0.5 liters

• 5 liters

• 50 liters

• 500 liters

Answer explanation

A small water bottle that holds about 500 ml is equivalent to 0.5 liters, since 1 liter equals 1000 ml. Therefore, the correct choice is 0.5 liters.

Tags

CCSS.4.MD.A.1

• 12 cm³

• 24 cm³

• 20 cm³

• 18 cm³

Answer explanation

To find the volume of the rectangular prism, use the formula V = l × w × h. Substituting the values: V = 4 cm × 3 cm × 2 cm = 24 cm³. Therefore, the correct answer is 24 cm³.

Tags

CCSS.7.G.B.6

• Cube

• Sphere

• Both have the same volume

• Cannot be determined

Answer explanation

The volume of the cube is 2^3 = 8 cm³. The volume of the sphere is (4/3)π(1^3) ≈ 4.19 cm³. Since 8 cm³ > 4.19 cm³, the cube has a greater volume.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

• 141.3 cm³

• 47.1 cm³

• 94.2 cm³

• 188.4 cm³

Answer explanation

The volume of a cylinder is calculated using the formula V = πr²h. Substituting r = 3 cm and h = 5 cm, we get V = 3.14 * (3)² * 5 = 141.3 cm³. Thus, the correct answer is 141.3 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Identify the correct formula for the volume of a cone.

Answer explanation

The volume of a cone is calculated using the formula V = \frac{1}{3} \pi r^2 h. This formula accounts for the cone's shape, where the volume is one-third that of a cylinder with the same base and height.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Convert 1500 cubic centimeters to liters.

• 1.5 liters

• 15 liters

• 0.15 liters

• 150 liters

Answer explanation

To convert cubic centimeters to liters, divide by 1000. Thus, 1500 cm³ ÷ 1000 = 1.5 liters. Therefore, the correct answer is 1.5 liters.

Tags

CCSS.5.MD.A.1

Estimate the volume of a large suitcase that is approximately 80 cm long, 50 cm wide, and 30 cm high.

• 12,000 cm³

• 120,000 cm³

• 1,200 cm³

• 120 cm³

Answer explanation

To estimate the volume of the suitcase, multiply its dimensions: 80 cm (length) x 50 cm (width) x 30 cm (height) = 120,000 cm³. Thus, the correct answer is 120,000 cm³.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2